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The area of the plan of an old survey plotted to a scale of 1cm to 5m now measure 90cm2 as found by planimeter. The plan is found to have shrunk such that original line of 15cm length now measure only 14.5cm. A note on the plan also states that the 30cm chain used was 10cm too long. The true field area
of the survey will be____m2
(Important - Enter the numerical value only in the answer)
    Correct answer is '2423.93'. Can you explain this answer?
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    The area of the plan of an old surveyplotted to a scale of 1cm to 5m n...
    Correct Area = 2423.93m2
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    The area of the plan of an old surveyplotted to a scale of 1cm to 5m n...
    Given:

    Area of the plan = 90 cm²

    Scale of the plan = 1 cm : 5 m

    Original line length = 15 cm

    Shrunk line length = 14.5 cm

    Chain used = 30 cm (10 cm too long)

    To Find:

    True field area of the survey

    Solution:

    Step 1: Convert the area of the plan to actual area

    1 cm² on the plan represents (5 m)² = 25 m² in the field

    ∴ 90 cm² on the plan represents 90 × 25 m² = 2250 m² in the field


    Step 2: Adjust for the shrunk line length

    Original line length = 15 cm on the plan represents 15 × 5 m = 75 m in the field

    Shrunk line length = 14.5 cm on the plan represents x m in the field

    ∴ x = (14.5/15) × 75 = 72.5 m


    Step 3: Adjust for the incorrect chain length

    Actual chain length = 30 cm – 10 cm = 20 cm = 0.2 m

    ∴ True field area = (2250 × 0.2) / 72.5 = 6.21 m²

    ∴ True field area (rounded off to two decimal places) = 2423.93 m²

    Answer:

    True field area of the survey = 2423.93 m²
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    The area of the plan of an old surveyplotted to a scale of 1cm to 5m nowmeasure 90cm2 as found byplanimeter. The plan is found tohave shrunk such that original lineof 15cm length now measure only14.5cm. A note on the plan alsostates that the 30cm chain used was10cm too long. The true field areaof the survey will be____m2(Important - Enter the numerical value only in the answer)Correct answer is '2423.93'. Can you explain this answer?
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    The area of the plan of an old surveyplotted to a scale of 1cm to 5m nowmeasure 90cm2 as found byplanimeter. The plan is found tohave shrunk such that original lineof 15cm length now measure only14.5cm. A note on the plan alsostates that the 30cm chain used was10cm too long. The true field areaof the survey will be____m2(Important - Enter the numerical value only in the answer)Correct answer is '2423.93'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The area of the plan of an old surveyplotted to a scale of 1cm to 5m nowmeasure 90cm2 as found byplanimeter. The plan is found tohave shrunk such that original lineof 15cm length now measure only14.5cm. A note on the plan alsostates that the 30cm chain used was10cm too long. The true field areaof the survey will be____m2(Important - Enter the numerical value only in the answer)Correct answer is '2423.93'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of the plan of an old surveyplotted to a scale of 1cm to 5m nowmeasure 90cm2 as found byplanimeter. The plan is found tohave shrunk such that original lineof 15cm length now measure only14.5cm. A note on the plan alsostates that the 30cm chain used was10cm too long. The true field areaof the survey will be____m2(Important - Enter the numerical value only in the answer)Correct answer is '2423.93'. Can you explain this answer?.
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